Learn on PengiEureka Math, Grade 4Chapter 27: Repeated Addition of Fractions as Multiplication

Lesson 4: Find the product of a whole number and a mixed number using the distributive property.

In this Grade 4 Eureka Math lesson from Chapter 27, students learn to find the product of a whole number and a mixed number by applying the distributive property to decompose the mixed number into its whole and fractional parts. Students practice expressions such as 4 × 9¾ by breaking them into (4 × 9) + (4 × ¾) and combining the results into a single mixed number or whole number. Tape diagrams and number lines are used throughout to support understanding of the multiplication process.

Section 1

Multiply a Whole Number and a Mixed Number Using the Distributive Property

Property

To multiply a whole number by a mixed number, decompose the mixed number into a sum of its whole and fractional parts. Then, apply the distributive property.

a×(b+cd)=(a×b)+(a×cd)a \times (b + \frac{c}{d}) = (a \times b) + (a \times \frac{c}{d})

Examples

Book overview

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Chapter 27: Repeated Addition of Fractions as Multiplication

  1. Lesson 1

    Lesson 1: Represent the multiplication of n times a/b as (n x a)/b using the associative property and visual models.

    LearnPractice
  2. Lesson 2

    Lesson 2: Represent the multiplication of n times a/b as (n x a)/b using the associative property and visual models.

    LearnPractice
  3. Lesson 3

    Lesson 3: Find the product of a whole number and a mixed number using the distributive property.

    LearnPractice
  4. Lesson 4Current

    Lesson 4: Find the product of a whole number and a mixed number using the distributive property.

    LearnPractice
  5. Lesson 5

    Lesson 5: Solve multiplicative comparison word problems involving fractions.

    LearnPractice
  6. Lesson 6

    Lesson 6: Solve word problems involving the multiplication of a whole number and a fraction including those involving line plots.

    LearnPractice

Lesson overview

Expand to review the lesson summary and core properties.

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Section 1

Multiply a Whole Number and a Mixed Number Using the Distributive Property

Property

To multiply a whole number by a mixed number, decompose the mixed number into a sum of its whole and fractional parts. Then, apply the distributive property.

a×(b+cd)=(a×b)+(a×cd)a \times (b + \frac{c}{d}) = (a \times b) + (a \times \frac{c}{d})

Examples

Book overview

Jump across lessons in the current chapter without opening the full course modal.

Continue this chapter

Chapter 27: Repeated Addition of Fractions as Multiplication

  1. Lesson 1

    Lesson 1: Represent the multiplication of n times a/b as (n x a)/b using the associative property and visual models.

    LearnPractice
  2. Lesson 2

    Lesson 2: Represent the multiplication of n times a/b as (n x a)/b using the associative property and visual models.

    LearnPractice
  3. Lesson 3

    Lesson 3: Find the product of a whole number and a mixed number using the distributive property.

    LearnPractice
  4. Lesson 4Current

    Lesson 4: Find the product of a whole number and a mixed number using the distributive property.

    LearnPractice
  5. Lesson 5

    Lesson 5: Solve multiplicative comparison word problems involving fractions.

    LearnPractice
  6. Lesson 6

    Lesson 6: Solve word problems involving the multiplication of a whole number and a fraction including those involving line plots.

    LearnPractice